Numerical stability of a hybrid method for pricing options

TL;DR

This paper introduces a hybrid numerical method combining tree and finite-difference techniques to efficiently and accurately price European and American options under a complex Bates jump model with stochastic interest rates.

Contribution

The paper presents a novel hybrid approach that integrates tree methods and finite-difference schemes for stable and precise option pricing in advanced stochastic models.

Findings

Methods achieve high accuracy in European and American option pricing.

Algorithms demonstrate reliability and computational efficiency.

Numerical experiments validate the stability and effectiveness of the proposed approach.

Abstract

We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a finite-difference approach in order to handle the underlying asset price process. We also propose hybrid simulations for the model, following a binomial tree in the direction of both the volatility and the interest rate, and a space-continuous approximation for the underlying asset price process coming from a Euler-Maruyama type scheme. We show that our methods allow to obtain efficient and accurate European and American option prices. Numerical experiments are provided, and show the reliability and the efficiency of the algorithms.